A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion

By Joachim Weickert, Christoph Schnörr. International Journal of Computer Vision, 2001

344 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/b9065f8b59f6c254d29f7a48afb0c4d15e5db28b

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In Computer Vision and Pattern Recognition

Citations in the corpus

High Accuracy Optical Flow Estimation Based on a Theory for Warping (2004, methodology): “In order to handle discontinuities in the flow field, the quadratic regulariser in the Horn and Schunck model was replaced by smoothness constraints that permit piecewise smooth results [1, 9, 19, 21, 25].”
Motion Competition: A Variational Approach to Piecewise Parametric Motion Segmentation (2005, background): “Rather than first estimating local motion and subsequently segmenting or clustering regions with respect to the estimated motion (Wang and Adelson, 1994), some researchers have proposed to model motion discontinuities implicitly by non-quadratic robust estimators (Nagel and Enkelmann, 1986; Black an”
Fluid flow and optical flow (2008, methodology): “…mathematical analysis of the variational formulation of the brightness constraint equation has been given by Aubert, Deriche & Kornprobst (1999) and Weickert & Schnorr (2001), and the convergence of the numerical solution of the corresponding Euler–Lagrange equation has been proven by Mitiche &…”
Optical flow modeling and computation: A survey (2015, background): “The system (33) can be rewritten by introducing the diffusion tensor D accounting for the relation with diffusion equations [266]: @ q data ð x ; I 1 ; I 2 ; w Þ @ u (cid:2) k div D ð x Þ r u ð x Þ ð Þ ¼ 0 @ q data ð x ; I 1 ; I 2 ; w Þ @ v The analogy with diffusion equations makes explicit the…”
Variational Optic Flow Computation with a Spatio-Temporal Smoothness Constraint (2001, background): “For a more detailed account on image- and fiow-driven regularizers and a weIl-posedness framework for both types we refer to [36].”
Dense Estimation of Fluid Flows (2002, background): “See for instance [2], [9], [11], [25], [26], [27], [31], [44], [45] for the description of such state-of-the-art techniques and [5], [6] for comprehensive comparisons with completely different approaches.”